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The separation theorem for quasi-closed sets


Authors: John H. V. Hunt and Adalberto García-Máynez
Journal: Proc. Amer. Math. Soc. 27 (1971), 399-404
MSC: Primary 54.55
MathSciNet review: 0276930
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Abstract: The concepts of ``closed set, separation and $ n$-cell'' are generalized to ``quasi-closed set, weak separation and locally cohesive space,'' respectively. It is then proved that any quasiclosed set $ L$, which weakly separates two closed subsets $ A,B$ in a locally cohesive $ {T_1}$-space $ X$, contains a closed set $ K$ which separates $ A - K$ and $ B - K$ in $ X$.


References [Enhancements On Off] (What's this?)

  • [1] A. García-Máynez, Ph.D. Thesis, University of Virginia, Charlottesville, Va., 1968.
  • [2] Gordon T. Whyburn, Loosely closed sets and partially continuous functions, Michigan Math. J. 14 (1967), 193–205. MR 0208578
  • [3] Gordon T. Whyburn, Quasi-closed sets and fixed points, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 201–205. MR 0210111
  • [4] G. T. Whyburn, assisted by J. H. V. Hunt, Notes on functions and multifunctions, University of Virginia, Charlottesville, Va., 1966/67 (mimeographed notes).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0276930-2
Keywords: Quasi-closed set, canonical region, locally cohesive space weak separation
Article copyright: © Copyright 1971 American Mathematical Society